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Simplifying 4166 = 2(3.14) * r2 + 2(3.14) * r(89) Multiply 2 * 3.14 4166 = 6.28r2 + 2(3.14) * r(89) Reorder the terms for easier multiplication: 4166 = 6.28r2 + 2 * 3.14 * 89r Multiply 2 * 3.14 4166 = 6.28r2 + 6.28 * 89r Multiply 6.28 * 89 4166 = 6.28r2 + 558.92r Reorder the terms: 4166 = 558.92r + 6.28r2 Solving 4166 = 558.92r + 6.28r2 Solving for variable 'r'. Reorder the terms: 4166 + -558.92r + -6.28r2 = 558.92r + -558.92r + 6.28r2 + -6.28r2 Combine like terms: 558.92r + -558.92r = 0.00 4166 + -558.92r + -6.28r2 = 0.00 + 6.28r2 + -6.28r2 4166 + -558.92r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 4166 + -558.92r + -6.28r2 = 0.00 Begin completing the square. Divide all terms by -6.28 the coefficient of the squared term: Divide each side by '-6.28'. -663.3757962 + 89r + r2 = 0 Move the constant term to the right: Add '663.3757962' to each side of the equation. -663.3757962 + 89r + 663.3757962 + r2 = 0 + 663.3757962 Reorder the terms: -663.3757962 + 663.3757962 + 89r + r2 = 0 + 663.3757962 Combine like terms: -663.3757962 + 663.3757962 = 0.0000000 0.0000000 + 89r + r2 = 0 + 663.3757962 89r + r2 = 0 + 663.3757962 Combine like terms: 0 + 663.3757962 = 663.3757962 89r + r2 = 663.3757962 The r term is 89r. Take half its coefficient (44.5). Square it (1980.25) and add it to both sides. Add '1980.25' to each side of the equation. 89r + 1980.25 + r2 = 663.3757962 + 1980.25 Reorder the terms: 1980.25 + 89r + r2 = 663.3757962 + 1980.25 Combine like terms: 663.3757962 + 1980.25 = 2643.6257962 1980.25 + 89r + r2 = 2643.6257962 Factor a perfect square on the left side: (r + 44.5)(r + 44.5) = 2643.6257962 Calculate the square root of the right side: 51.41620169 Break this problem into two subproblems by setting (r + 44.5) equal to 51.41620169 and -51.41620169.Subproblem 1
r + 44.5 = 51.41620169 Simplifying r + 44.5 = 51.41620169 Reorder the terms: 44.5 + r = 51.41620169 Solving 44.5 + r = 51.41620169 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-44.5' to each side of the equation. 44.5 + -44.5 + r = 51.41620169 + -44.5 Combine like terms: 44.5 + -44.5 = 0.0 0.0 + r = 51.41620169 + -44.5 r = 51.41620169 + -44.5 Combine like terms: 51.41620169 + -44.5 = 6.91620169 r = 6.91620169 Simplifying r = 6.91620169Subproblem 2
r + 44.5 = -51.41620169 Simplifying r + 44.5 = -51.41620169 Reorder the terms: 44.5 + r = -51.41620169 Solving 44.5 + r = -51.41620169 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-44.5' to each side of the equation. 44.5 + -44.5 + r = -51.41620169 + -44.5 Combine like terms: 44.5 + -44.5 = 0.0 0.0 + r = -51.41620169 + -44.5 r = -51.41620169 + -44.5 Combine like terms: -51.41620169 + -44.5 = -95.91620169 r = -95.91620169 Simplifying r = -95.91620169Solution
The solution to the problem is based on the solutions from the subproblems. r = {6.91620169, -95.91620169}
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